Rewrite as a simplified fraction. ${1.14\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1142.2222...\\ 100x &= 114.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1028}$ ${x = \dfrac{1028}{900}} $ ${x = \dfrac{257}{225}} \text{or} {1 \dfrac{32}{225}}$